Square Nanometers to Square Centimeters conversion

How to convert square nanometers to square centimeters?

To convert from square nanometers (nm²) to square centimeters (cm²), you'll need to understand the conversion between the units of measure for length first:

1 nanometer (nm) = $1 \times 10^{-9}$ meters (m) 1 centimeter (cm) = $1 \times 10^{-2}$ meters (m)

Now, to convert from square nanometers to square centimeters, you need to square the conversion factor between nanometers and centimeters:

$\left(1 \, \text{nm}\right)^2 = \left(1 \times 10^{-9} \, \text{m}\right)^2 = 1 \times 10^{-18} \, \text{m}^2$

$\left(1 \, \text{cm}\right)^2 = \left(1 \times 10^{-2} \, \text{m}\right)^2 = 1 \times 10^{-4} \, \text{m}^2$

To find the conversion factor between square nanometers and square centimeters:

$1 \, \text{cm}^2 = 1 \times 10^{14} \, \text{nm}^2$

Therefore, to convert 1 square nanometer to square centimeters:

$1 \, \text{nm}^2 = \left( 1 \times 10^{-18} \, \text{m}^2 \right) \times \frac{1 \, \text{cm}^2}{1 \times 10^{-4} \, \text{m}^2}$

$1 \, \text{nm}^2 = 1 \times 10^{-18} \, \text{m}^2 \times 1 \times 10^4 \, \text{cm}^2 / \text{m}^2$

$1 \, \text{nm}^2 = 1 \times 10^{-14} \, \text{cm}^2$

So, $1 \text{ square nanometer} = 1 \times 10^{-14} \text{ square centimeters}$.

Real-world examples of quantities of square nanometers

1. Surface Area of Nanoparticles:

   • Many nanoparticles have sizes that are within a range of a few nanometers. For example, a gold nanoparticle with a surface area of approximately 100 nm² can be converted to square centimeters: $100 \, \text{nm}^2 = 100 \times 10^{-14} \, \text{cm}^2 = 1 \times 10^{-12} \, \text{cm}^2$

2. Microchip Component Size:

   • Modern microprocessors have transistor gates that are on the order of tens of nanometers. For example, a transistor gate area might be around 20 nm x 20 nm = 400 nm²: $400 \, \text{nm}^2 = 400 \times 10^{-14} \, \text{cm}^2 = 4 \times 10^{-12} \, \text{cm}^2$

3. Biological Structures:

   • Certain biological structures, such as protein molecules, might have surface areas of several square nanometers. For instance, a protein binding site of 50 nm²: $50 \, \text{nm}^2 = 50 \times 10^{-14} \, \text{cm}^2 = 5 \times 10^{-13} \, \text{cm}^2$

These examples illustrate the types of situations where square nanometers are a useful unit of measure, especially in fields like nanotechnology, microelectronics, and molecular biology.